Stability and bifurcations in an epidemic model with varying immunity period.

@article{Blyuss2010StabilityAB,
  title={Stability and bifurcations in an epidemic model with varying immunity period.},
  author={Konstantin B. Blyuss and Yuliya N. Kyrychko},
  journal={Bulletin of mathematical biology},
  year={2010},
  volume={72 2},
  pages={
          490-505
        }
}
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is… CONTINUE READING

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